Can You Choose Your Own Constants in Differential Equations Integration?

gomes.
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Because it makes the coefficient of the term with t as 1 and 0 as the constant. It sort of makes the obtained general solution 'better' looking.
 
thanks, so you are allowed to set it to any number?
 
For that, it looks that way. Granted I did not really read through the equations thoroughly.
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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